### Quasi-Random PCP and Hardness of 2-Catalog Segmentation

Rishi Saket
We study the problem of 2-Catalog Segmentation which is one of the several variants of segmentation problems, introduced by Kleinberg et al., that naturally arise in data mining applications. Formally, given a bipartite graph $G = (U, V, E)$ and parameter $r$, the goal is to output two subsets $V_1, V_2 subseteq V$, each of size $r$, to maximize, $sum_{u \in U} max {|E(u, V_1)|, |E(u, V_2)|},$ where $E(u, V_i)$ is the set of edges...